MCQ
A possible value of $\tan \left(\frac{1}{4} \sin ^{-1} \frac{\sqrt{63}}{8}\right)$ is :
- ✓$\frac{1}{\sqrt{7}}$
- B$2 \sqrt{2}-1$
- C$\sqrt{7}-1$
- D$\frac{1}{2 \sqrt{2}}$
$\sin 4 \theta=\frac{\sqrt{63}}{8}$
$\cos 4 \theta=\frac{1}{8}$
$2 \cos ^{2} 2 \theta-1=\frac{1}{8}$
$\cos ^{2} 2 \theta=\frac{9}{16}$
$\cos 2 \theta=\frac{3}{4}$
$2 \cos ^{2} \theta-1=\frac{3}{4}$
$\cos ^{2} \theta=\frac{7}{8}$
$\cos \theta=\frac{\sqrt{7}}{2 \sqrt{2}}$
$\tan \theta=\frac{1}{\sqrt{7}}$
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